Population vs Sample: Definition, Differences [With Examples]

Understanding the distinction between “population” and “sample” in statistics is critical for accurate and trustworthy analysis. A sample is a subset of population, whereas a population refers to the entire collection of people, things, or events of interest. In order to illustrate the importance of population and sample in statistical analysis, this article seeks to offer a thorough review of their definitions, distinctions, and examples. By exploring the importance of accurate population definition and measurement, the role of sampling and sample size determination, and examples of statistical inference, we will delve into the fundamental concepts that underpin statistical research.

What is Population?

In statistics, a population refers to the entire set of individuals, objects, or events that are of interest to a researcher. It encompasses every element that possesses the characteristics under study. For instance, the population would be composed of every adult living in that country if we were looking at the average height of all adults in that nation.

A population’s main characteristic is that it is full and contains every member who satisfies the required standards. However, it is frequently difficult or impractical to gather data from the whole population owing to practical limitations including time, money, and accessibility. Here is where the idea of a sample is useful. To equip with expert knowledge and skills, head on to Master of Science in Machine Learning & AI from LJMU course. 

What is Sample?

A sample, in statistics, is a subset of a population. A smaller representative sample is chosen from the population to collect data and draw conclusions about the total population. We can infer information or make assumptions about the population as a whole by looking at the sample’s features.

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Population vs Sample

The main difference between a population and a sample lies in their size and inclusiveness. A population encompasses the entire group of interest, whereas a sample represents only a portion of that group. While the population is complete and includes all members, the sample is a subset that is chosen to represent the population.

Another difference between population and sample lies in the level of practicality. It is often impractical, if not impossible, to collect data from an entire population due to constraints such as time, cost, and logistics. Therefore, researchers rely on sampling distribution methods to gather data from a manageable subset of the population. This allows them to draw meaningful conclusions while reducing the resources required.

Similarities Between Population and Sample

Despite their differences, the population and sample share certain characteristics. Both contain individual elements or units that possess the characteristics being studied. They can be analyzed using statistical techniques to draw conclusions about the larger group. Additionally, both the population and sample can have specific parameters or statistics associated with them, which can provide valuable insights into the characteristics of interest. To get a detailed understanding of these topics, you can opt for Executive PG Program in Data Science & Machine Learning from university of Maryland.

Importance of Accurate Population Definition and Measurement (Under Population)

Defining and accurately measuring the population of interest is vital in statistical analysis. A clear population definition ensures that the research objectives are well-defined and align with the intended scope. Moreover, precise population measurement enables researchers to estimate population parameters, which are numerical characteristics of the entire population. For example, if a pharmaceutical company is developing a new drug, understanding the population of patients who may benefit from it is crucial for successful product development and marketing.

Importance of Accurate Sampling and Sample Size Determination (Under Sample)

In statistical analysis, sampling—the act of choosing a portion of the population — is an important step. Making sure the sample is representative of the population, or appropriately reflects the diversity and features of the broader group, is essential to sampling. Because the sample is representative, conclusions and generalizations about the population as a whole may be drawn from it. To balance accuracy and efficiency, it is crucial to choose the right sample size. A sparse sample could not yield enough data to draw valid conclusions, whereas an excessively large sample might be time- and money-consuming without adding anything.

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Population and Sample Formulas

When dealing with populations and samples, various formulas are used to calculate parameters and statistics. These formulas differ depending on whether the data is collected from the entire population or a sample.

Collecting Data from a Population

The parameters of interest can be derived directly from the complete dataset while gathering data from a population. To get the mean height of all students at a school, for instance, the heights of each student would be measured, and the mean would be computed using the following formula:

Population Mean (μ) = Σ x / N

Here, Σx represents the sum of all individual values in the population, and N represents the total number of units in the population.

Collecting Data from a Sample

The statistics computed are used to estimate the population’s parameters when data from a sample is collected. For instance, if a researcher chooses a sample of 100 kids from a school, the formula for calculating the mean height is as follows:

Sample Mean Symbol (x̄) = Σ x / n

In this formula, Σ x represents the sum of all individual values in the sample, and n represents the sample size.

Reasons for Sampling

Sampling is employed for various reasons in statistical analysis. Some common reasons for using sampling instead of studying the entire population include:

1. Cost and Time Efficiency: Collecting data from an entire population can be time-consuming and expensive. Sampling allows researchers to obtain reliable information with fewer resources.
2. Infeasibility: In certain cases, it may be practically impossible to study the entire population due to its size or geographical dispersion. Sampling provides a more feasible approach to studying such populations.
3. Destructive Testing: When the process of collecting data involves destructive testing or consumes the resources being measured, sampling allows researchers to preserve the population while still obtaining valuable information.

Examples of Statistical Inference Using Population and Sample Data

To illustrate the use of population and sample data in statistical inference, consider the following examples:

Example 1: Calculating a city’s median household income

Consider a scenario where a researcher wishes to calculate the mean income of all working people in a specific city. Due to time and resource limitations, it might not be possible to collect data from the full population. Instead, the researcher chooses a random sample of 500 working persons and gathers information on their earnings. The researcher can make an educated guess as to the average income of the total population by computing the sample mean and applying statistical methods like confidence intervals.

Example 2: Hypothesis Testing in Medicine

Population and sample data are essential for evaluating hypotheses in medical research. Imagine that researchers are comparing the efficacy of a new medicine to one that already exists to treat a certain ailment. They choose a sample of people who have the illness and randomly divide them into two groups, one of whom receives the new medication and the other the current medication. Statistical tests may be run to determine if the new treatment is considerably more successful than the current drug in the population by comparing the results in the sample, such as the recovery rate or symptom improvement.

Population Parameter vs Sample Statistic

In statistical analysis, population parameters and sample statistics are used to describe the characteristics of the population and sample, respectively. A population parameter represents a numerical value that describes a particular characteristic of the population. For example, the population mean represents the average value of a variable in the population.

A sample statistic, on the other hand, is a numerical number that describes a specific attribute of the sample. The sample mean, for example, reflects the average value of a variable in the sample. Sample statistics are used to estimate population parameters, allowing researchers to make population conclusions.

Conclusion

Understanding the distinctions between population and sample is crucial for conducting accurate and reliable statistical analyses. A population represents the complete group of interest, whereas a sample is a subset chosen from the population. Accurate population definition and measurement, as well as adequate sampling methodologies, are required for relevant findings. Researchers can establish reasonable conclusions about the wider population based on the features found in the sample by using population factors and sample statistics. Learn various techniques and strategies via MS in Full Stack AI and ML course from upGrad.